Micro-Doppler Effect of a Rotating Object with a Doppler Radar

This is an example of using RadarSimPy to simulate the micro-Doppler effect of a rotating turbine with a Doppler radar. Ray-Tracing/Shoot-and-Bounce-Rays method is used in RadarSimPy. The ray-tracing engine RadarSimC, which is built with C++, is integrated in RadarSimPy.

RadarSimPy is a radar simulation package built with python. Contact me if you are interested in this module.

This notebook is available on my GitHub.

Radar Model

Transmitter

The following table lists the basic parameters of the radar transmitter.

Parameter Variable in RadarSimPy Value
Center frequency ($f_c$) fc 24.125 GHz
Transmitted power ($P_t$) tx_power 10 dBm
Signal length ($T$) pulse_length 2 s

Receiver

The parameters of the receiver are listed in the table below.

Parameter Variable in RadarSimPy Value
Sampling rate ($f_s$) fs 400 sps
Noise figure ($NF$) noise_figure 20 dB
RF gain/loss ($G_{rf}$) rf_gain 20 dB
Baseband gain ($G_{BB}$) baseband_gain 50 dB
Load resistor ($R_L$) load_resistor 1000 $\Omega$

Aperture

The radar aperture to receive the reflected rays.

Parameter Physical Meaning
phi Angle phi of the aperture normal (degree)
theta Angle theta of the aperture normal (degree)
location Center location of the aperture (x, y, z) m
extension Extension of the aperture (left, right, top, bottom) m
In [1]:
import numpy as np
from radarsimpy import Radar, Transmitter, Receiver

import matplotlib.pyplot as plt

tx = Transmitter(fc=24.125e9,
                 tx_power=10,
                 pulse_length=12,
                 pulses=1,
                 channels=[dict(location=(0, 0, 0))])

rx = Receiver(fs=400,
              noise_figure=12,
              rf_gain=20,
              baseband_gain=50,
              load_resistor=1000,
              channels=[dict(location=(0, 0, 0))])


radar = Radar(transmitter=tx, receiver=rx)

aperture = dict(
    phi=0,
    theta=90,
    location=[0, 0, 0],
    extension=[0.1, 0.1, 0.1, 0.1]
)

radar = Radar(transmitter=tx, receiver=rx, aperture=aperture)

Target Model

Load the stl model of the target and set the location, speed, rotation, and rotation_rate of the target.

  • location: (x, y, z) m
  • speed: (x, y, z) m/s
  • rotation: (yaw, pitch, roll) degree
  • rotation_rate: (yaw, pitch, roll) degree/s

In this simulation, the target is a 3-blade turbine. The turbine is rotating along the y-axis with -20 degree/s.

In [2]:
target_1 = {
    'model': '../models/fan_3blade.stl',
    'location': (30, 0, 0),
    'rotation': (0, -10, 0),
    'rotation_rate': (0, 20, 0),
    'speed': (0, 0, 0)
}

targets = [target_1]
In [3]:
from stl import mesh
import plotly.graph_objs as go
from plotly.offline import iplot

mesh_data = mesh.Mesh.from_file(target_1['model'])

x = np.ravel(mesh_data.vectors[:, :, 0])
y = np.ravel(mesh_data.vectors[:, :, 1])
z = np.ravel(mesh_data.vectors[:, :, 2])

plate = go.Mesh3d(x=x, y=y, z=z, opacity=1,
                  i=np.arange(0, np.shape(mesh_data.vectors)[0]*3, 3),
                  j=np.arange(1, np.shape(mesh_data.vectors)[0]*3, 3),
                  k=np.arange(2, np.shape(mesh_data.vectors)[0]*3, 3),
                  )

layout = go.Layout(
    title='Model',
    scene=dict(
        aspectmode='data',
    ),
    margin=dict(l=0, r=0, b=0, t=40)
)

fig = go.Figure(data=[plate], layout=layout)
iplot(fig)

Ray Tracing

Simulate rays. level='sample' defines ray tracing for each sample point.

In [4]:
from radarsimpy import scene

data = scene(radar, targets, correction=-42, density=1, level='sample')
baseband = data['baseband']
timestamp = data['timestamp']
In [5]:
beat_I = go.Scatter(
    x=timestamp[0, 0, :],
    y=np.real(baseband[0, 0, :]),
    name='I',
)
beat_Q = go.Scatter(
    x=timestamp[0, 0, :],
    y=np.imag(baseband[0, 0, :]),
    name='Q',
)
data = [beat_I, beat_Q]

layout = go.Layout(
    title='I/Q Baseband Signals',
    yaxis=dict(title='Amplitude (V)'),
    xaxis=dict(title='Time (s)'),
)

fig = go.Figure(data, layout=layout)
iplot(fig)

Short-Time Fourier Transform

In [6]:
from scipy.signal import stft

spec = stft(baseband[0, 0, :], fs=radar.receiver.fs,
            nperseg=64, noverlap=40, nfft=128, return_onesided=False)
In [7]:
idx_neg = np.where(spec[0] < 0)
idx_pos = np.where(spec[0] >= 0)

dopp_ordered = spec[0][np.concatenate([idx_neg[0], idx_pos[0]])]

spec_shifted = spec[2][np.concatenate([idx_neg[0], idx_pos[0]]), :]

data = go.Heatmap(
    z=20*np.log10(np.abs(spec_shifted)),
    x=spec[1],
    y=dopp_ordered,
    hoverongaps=False,
    colorscale='Jet')

layout = go.Layout(
    yaxis=dict(title='Doppler (Hz)'),
    xaxis=dict(title='Time (s)'),
    margin=dict(l=0, r=0, b=0, t=20)
)

fig = go.Figure(data=data, layout=layout)
iplot(fig)